Nuprl Lemma : base-member-partial
∀[A:Type]. ∀[a:Base]. (a ∈ partial(A)) supposing ((¬is-exception(a)) and a ∈ A supposing (a)↓) supposing value-type(A)
Proof
Definitions occuring in Statement :
partial: partial(T),
value-type: value-type(T),
has-value: (a)↓,
is-exception: is-exception(t),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
prop: ℙ,
base-partial: base-partial(T),
and: P ∧ Q,
cand: A c∧ B,
partial: partial(T),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q
Lemmas referenced :
has-value_wf_base,
equal-wf-base,
base_wf,
value-type_wf,
not_wf,
is-exception_wf,
base-partial_wf,
per-partial_wf,
per-partial-equiv_rel,
per-partial-reflex,
quotient-member-eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
sqequalRule,
Error :isectIsType,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
independent_pairFormation,
productEquality,
isectEquality,
lambdaEquality,
setElimination,
rename,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[A:Type]
\mforall{}[a:Base]. (a \mmember{} partial(A)) supposing ((\mneg{}is-exception(a)) and a \mmember{} A supposing (a)\mdownarrow{}) supposing valu\000Ce-type(A)
Date html generated:
2019_06_20-PM-00_33_52
Last ObjectModification:
2018_09_26-PM-01_16_40
Theory : partial_1
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